Sept. 6, 1883] 



NATURE 



435 



book is rendered more complete by a short account of 

 Italian health resorts, Algiers, Egypt, Madeira, and Tene- 

 riffe. The book will be useful both to invalids who are 

 meditating a winter abroad and to medical men by aiding 

 them in the selection of the proper places to which to 

 send patients. 



Dr. Bare"ty's description of Nice and its climate is 

 naturally very much fuller than Dr. Marcet's, and while 

 the latter is a useful guide to the selection of a health 

 resort, the former will be of great service to those who 

 have already fixed upon Nice. The climate of this town 

 varies very much in its different parts, and the proper 

 selection of an hotel or residence is of considerable im- 

 portance. As a guide in this, and also as a general hand- 

 book for reference when residing in the town, Dr. Bare'ty's 

 book is to be recommended. 



Vichy and its Therapeutical Resources. By Prosser 

 James, M.D., M.R.C.P., &c. Fifth Edition. Pp.84. 

 (London: Bailliere, Tyndall, and Cox, 1883.) 



This is a small guide-book to Vichy, pleasantly written. 

 It contains, as usual in such books, a general account of 

 the place, its springs bathing establishments and en- 

 virons, analyses of the waters, and an enumeration of the 

 diseases in which they are said to be useful. We doubt 

 whether the latter part will be of very much service either 

 to medical men or to invalids ; it might, we think, have 

 been omitted with advantage. 



LETTERS TO THE EDITOR 



\ The Editor does not hold himself responsible for opinions expressed 

 by his correspondents. Neither can he undertake to return, 

 or to correspond with the writers of, rejected manuscripts. 

 No notice is taken of anonymous communications. 

 The Editor urgently requests correspondents to keep their letters 

 as short as possible. The pressure on his space is so great 

 that it is impossible otherwise to insure the appearance even 

 of communications containing interesting and novel /acts.] 



Arithmetic Notation of Kinship 



Many writers have endeavoured to devise a simple method 

 of describing the various forms of kinship, which, when 

 expressed verbally, are cumbrous and puzzling in the highest 

 degree. I suspect, however, that if we hart always been 

 as familiar with the binary system of arithmetic as we are 

 with the decimal, that the facilities afforded by a numerical 

 system of notation of kinship would have been so obvious 

 that it would have been adopted as a matter of c >urse. The 

 notation I am about to propose is numerical, but it is not 

 binary. It however contains implicitly, as we shall see, owing 

 to the law s that govern numbers, the most important advantages 

 of the binary notation, and it seems better to begin to explain it 

 from the latter point of view. 



The number of direct ancestors that a person has in successive 

 generations is . . . 2*, 2 3 , 2'-, 2 1 , followed by 2" for himself, 

 the corresponding binary notations being 10,000, 1000, 100, 10, 

 1 respectively. We also see on a little reflection that, this being 

 the case, every direct ancestor in the «th degree admits of being 

 specified by a particular number, consisting of « 4- 1 places of 

 figures. Thus the two parents may be represented by 10 and II, 

 the four grandparents by 100, 101, no, in, and so on. Let us 

 draw up two schemes of ancestral roots, identical in arrange- 

 ment, but using in the one the symbols of/ for " the father of," 

 and m for "the mother of," and employing binary notation in 

 the other : — 



child 



ff 



'"/ 



fm 



100 



III 



1000 1001 1010 ion 1100 noi mo mi 

 &c. &c. 



We see (a) that if we disregard the child, and speak only of 

 his or her ancestry, all the even numbers apply to one sex and 

 all the odd ones to the other ; (b) that each term is derived from 

 its ancestral terms in so simple a way that it carries on its face 

 every step in the line of descent, however long it may be, through 

 which each ancestor is related to the child. Therefore, as I began 

 by saying, if we were familiar with decimal notation, we should 

 long since have described each form of ancestry by it. Instead of 

 saying that " B was a grandmoiher, namely, a father's mother 

 of A," we should have said "B was 101 of A." Or again, 

 instead of saying that " C was first cousin once removed to D, 

 the father's father's parents of C being the mother's parents of D," 

 we should have said " the 1000-1 of C are the 110-1 of D." The 

 case might have been one of half-blood, say by the father's ^ide, 

 then "the 1000 of C would be the no of D," a notation which 

 grows in simplicity as the verbal equivalent grows in complexity. 



Being, however, unfamiliar with binary notation, we fall back 

 on the decimnl, and translate the above numbers into their 

 equivalents, which are those I propose for the arithmetic notation 

 of kinship, as entered in the table below. 



Table of Ancestral Roots 



The sex of I is unspecified, it is equivalent to the word " child," 

 but all other odd numbers refer to females, and all even numbers 

 refer to males. If n is the register number of any ancestor, the 

 register numbers of his parents are 2n and 211 + I, We can thus 

 construct or analyse any register number with great facility. It 

 is not worth while giving an example of construction, but I 

 may give one of analysis. I write down the number and append 

 to it a series of successive halvings, so far as the numbers are, or 

 come out, even ; otherwise I substract I before taking their 

 halves. Then I write f (= father of), or m (= mother of), as 

 the case may be, below each entry. Let 253 be the number, 

 then I get — 



253 126 63 31 15 7 3 child 

 m f m m m m m child 



For purposes of exhaustive inquiry into the antecedents of a 

 family, this notation has the advantage of an index, and of 

 showing very compendiously how much has been done, and how 

 much remains to do. Francis Galton 



ff/ m ff fmf mmf ffm mfm fmm mmm 



etc. &C 



" Stachys palustris" as Food 



There is no r< ason to think that Stachys palustris, L., is 

 anywhere used now for food in the British Isles. The cultiva- 

 tion of the potato must have long since put it out of court for 

 any such purpose. But that it was once so employed there 

 seems al'undant evidence. The part eaten, however, was not 

 the "rhizomes," but the subterranean tubers. That the use of 

 these is now quite forgotten may be inferred from the fact that 

 the tubers themselves are not even mentioned in standard sys- 

 tematic books. Vet Irmisch (see Botanical Gazette, vol. ii. p. 

 293) gives the potato and Stachys palustris as well known in- 

 stances of dicotyledonous plants producing stem tubers which 

 become detached by the dying away of the older parts of the 

 parent plant which iroduced them. 



Johnson, in the second edition of Gerarde's " Herbal" (1636), 

 has nothing to say about the edibleness of the tubers. But he 



